{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:62OZRJ6K664TWMU6KFGGUX3SVV","short_pith_number":"pith:62OZRJ6K","schema_version":"1.0","canonical_sha256":"f69d98a7caf7b93b329e514c6a5f72ad753a7e54c7af6688a54b7e4db4097182","source":{"kind":"arxiv","id":"1803.09773","version":1},"attestation_state":"computed","paper":{"title":"The weighted moduli spaces of sextics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Lubjana Beshaj, Scott Guest","submitted_at":"2018-03-26T18:09:51Z","abstract_excerpt":"We use the weighted moduli height as defined in \\cite{sh-h} to investigate the distribution of fine moduli points in the moduli space of genus two curves.\n  We show that for any genus two curve with equation $y^2=f(x)$, its weighted moduli height $\\mathfrak h (\\mathfrak{p}) \\leq 2^3 \\sqrt{3 \\cdot 5 \\cdot 7} \\, \\cdot H(f)$, where $H(f)$ is the minimal naive height of the curve as defined in \\cite{height}. Based on the weighted moduli height $\\mathfrak h$ we create a database of genus two curves defined over $\\mathbb Q$ with small $\\mathfrak h$ and show that for small such height ($\\mathfrak h <"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1803.09773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-26T18:09:51Z","cross_cats_sorted":[],"title_canon_sha256":"a21a1f42ec91d02bc128d89aae4d69d8d9de176238f5e7e9cb361a7f6e158039","abstract_canon_sha256":"55ac02240ab8fab281a9dd29557f9ba1f375725b5bf2b7c24c3ced83e22135b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:10.541639Z","signature_b64":"sJbki8M2lj51p07p2uMufy9y+wnzuxD4y/74fY6LHr/5FvqwtYUcDzxLUVv/aFYQziBnDvAaoaQdF6QVw+koDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f69d98a7caf7b93b329e514c6a5f72ad753a7e54c7af6688a54b7e4db4097182","last_reissued_at":"2026-05-18T00:20:10.540942Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:10.540942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The weighted moduli spaces of sextics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Lubjana Beshaj, Scott Guest","submitted_at":"2018-03-26T18:09:51Z","abstract_excerpt":"We use the weighted moduli height as defined in \\cite{sh-h} to investigate the distribution of fine moduli points in the moduli space of genus two curves.\n  We show that for any genus two curve with equation $y^2=f(x)$, its weighted moduli height $\\mathfrak h (\\mathfrak{p}) \\leq 2^3 \\sqrt{3 \\cdot 5 \\cdot 7} \\, \\cdot H(f)$, where $H(f)$ is the minimal naive height of the curve as defined in \\cite{height}. Based on the weighted moduli height $\\mathfrak h$ we create a database of genus two curves defined over $\\mathbb Q$ with small $\\mathfrak h$ and show that for small such height ($\\mathfrak h <"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09773","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.09773","created_at":"2026-05-18T00:20:10.541051+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.09773v1","created_at":"2026-05-18T00:20:10.541051+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09773","created_at":"2026-05-18T00:20:10.541051+00:00"},{"alias_kind":"pith_short_12","alias_value":"62OZRJ6K664T","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"62OZRJ6K664TWMU6","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"62OZRJ6K","created_at":"2026-05-18T12:32:08.215937+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/62OZRJ6K664TWMU6KFGGUX3SVV","json":"https://pith.science/pith/62OZRJ6K664TWMU6KFGGUX3SVV.json","graph_json":"https://pith.science/api/pith-number/62OZRJ6K664TWMU6KFGGUX3SVV/graph.json","events_json":"https://pith.science/api/pith-number/62OZRJ6K664TWMU6KFGGUX3SVV/events.json","paper":"https://pith.science/paper/62OZRJ6K"},"agent_actions":{"view_html":"https://pith.science/pith/62OZRJ6K664TWMU6KFGGUX3SVV","download_json":"https://pith.science/pith/62OZRJ6K664TWMU6KFGGUX3SVV.json","view_paper":"https://pith.science/paper/62OZRJ6K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.09773&json=true","fetch_graph":"https://pith.science/api/pith-number/62OZRJ6K664TWMU6KFGGUX3SVV/graph.json","fetch_events":"https://pith.science/api/pith-number/62OZRJ6K664TWMU6KFGGUX3SVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/62OZRJ6K664TWMU6KFGGUX3SVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/62OZRJ6K664TWMU6KFGGUX3SVV/action/storage_attestation","attest_author":"https://pith.science/pith/62OZRJ6K664TWMU6KFGGUX3SVV/action/author_attestation","sign_citation":"https://pith.science/pith/62OZRJ6K664TWMU6KFGGUX3SVV/action/citation_signature","submit_replication":"https://pith.science/pith/62OZRJ6K664TWMU6KFGGUX3SVV/action/replication_record"}},"created_at":"2026-05-18T00:20:10.541051+00:00","updated_at":"2026-05-18T00:20:10.541051+00:00"}